1. 물리 엔진 사용을 위한
게임 물리 프로그래밍 가이드
김성익(noerror@hitel.net)
2008/06/22

2. Overview
• 물리 엔진 사용을 위한 백그라운드 정보
– 개념들 소개/정리
– 구현을 다루지 않음
– Box2D 소개
• PhysX 소개

3. Box2D
• Erin Catto씨 개인 프로젝트
• 2D 오픈 소스 물리 엔진
• 사용한 프로젝트 : Crayon Physics
• http://www.box2d.org
• 최적의 물리 처리 레퍼런스

4. Kinematics
• Newtonian Physics
– F = ma
• Spring (F=-kx)
• Drag Force (F=-mpv)
• Gravity
– F = dp/dt, P = mv
– a = dV/dt
– V = dX/dt

5. Calculus
• Position
• Velocity
• Acceleration

6. Solution
• Analytic Solution
• Numeric Solution
– Euler Method
– Midpoint Method
– Runge Kutta
– Implicit Method
– Verlet

7. Solution
• Analytic Solution
• Numeric Solution
– Euler Method
– Midpoint Method
– Runge Kutta
– Implicit Method
– Verlet

8. Solution
• Analytic Solution
• Numeric Solution
– Euler Method
– Midpoint Method
– Runge Kutta
– Implicit Method
– Verlet

9. Solution
• Analytic Solution
• Numeric Solution
– Euler Method
– Midpoint Method
– Runge Kutta
– Implicit Method
– Verlet

10. Solution
• Analytic Solution
• Numeric Solution
– Euler Method
– Midpoint Method
– Runge Kutta
– Implicit Method
– Verlet

11. Rotational Dynamics
• Center of Mass
• Linear vs Angular
– Force vs Torque
– Mass vs Moment of inertia
– Momentum vs Angular Momentum
– Velocity vs Angular Velocity
– Position vs Orientation

12. Box2d CodeReview(1)
• Simulation iteration step
– broadphase
• 충돌검사 (충돌정보 Arbiter 개체로 저장)
– force 적용
• force->velocity
• torque->angular velocity
– prestep
• 충돌 포인트에 대해서 massnormal,
masstangent, bias 계산

13. Box2d CodeReview(2)
– 충돌에 의한 impulse
• 충돌체에 impulse
– velocity, angular velocity 적용
• Joint 에 의한 impulse
– 양 joint에 충돌체에 impulse
– 위치 및 회전에 적용
• velocity => position
• Angular velocity => rotation

14. PhysX(1)
• NVidia (http://www.ageia.com)
• 무료 (일부 플렛폼 및 소스코드 라이센스는
유료)
• 충실한 튜터리얼 셈플 제공
• 메인스트림 물리 엔진
• 사용 프로젝트 : 언리얼3, 외 다수

15. PhysX(2)
• 기능
– 복잡한 강체 물리 시스템
– 캐릭터 컨트롤
– 탈 것 다이나믹스
– 멀티쓰레드/멀티 플렛폼/PPU지원
– 유체 시뮬레이션
– 옷, 깃발등의 천 시뮬레이션
– 소프트 바디
– 역장(forcefield) 시뮬레이션

16. PhysX–architecture diagram

17. Shape
• Shape
– Sphere
– Capsule
– BoundBox
• AABB (Axis Aligned Bound Box)
• OBB (Object Oriented Box)
– Convex
– (height field)

18. PhysX-Shape
• Sphere
• Box
• Capsule
• Plane
• Height field
• Convex meshes
• Triangle meshes

19. PhysX-Actor

20. Collision Detection(1)
• Distance Test
– Point-point distance
– Line-point distance
– Line-line distance
– Segment-segment distance
• Rough Bounding
– Sweep and prune

21. Collision Detection(1)
• Distance Test
– Point-point distance
– Line-point distance
– Line-line distance
– Segment-segment distance
• Rough Bounding
– Sweep and prune

22. Collision Detection(2)
• SAT(separation axis test)
• Lin Canny
• Minkowski Diffrence

23. Collision Detection(2)
• SAT(separation axis test)
• Lin Canny
• Minkowski Diffrence

24. Collision Detection(2)
• SAT(separation axis test)
• Lin Canny
• Minkowski Sum/Diffrence

25. Collistion Detection(3)
• Determine Collision Time
– Time of impact
• Tunnelling (CCD)

26. Collistion Detection(3)
• Determine Collision Time
– Time of impact
• Tunnelling

27. PhysX - CCD
• Continuous Collision Detection

28. Collision Detection(4)
• Spatial Subdivision
– Bsp, k-d tree
– Portal
– Quad tree / octree
• Grouping
– Sleeping

29. Collision Detection(4)
• Spatial Subdivision
– Bsp, k-d tree
– Portal
– Quad tree / octree
• Grouping
– Sleeping

30. Collision Detection(4)
• Spatial Subdivision
– Bsp, k-d tree
– Portal
– Quad tree / octree
• Grouping
– Sleeping

31. Collision Detection(4)
• Spatial Subdivision
– Bsp, k-d tree
– Portal
– Quad tree / octree
• Grouping
– Sleeping

32. Collision Detection(4)
• Spatial Subdivision
– Bsp, k-d tree
– Portal
– Quad tree / octree
• Grouping
– Sleeping

33. PhysX-Collision Detection
• Contact Filtering
• Triggers
• CCD
• Dominance Grioup
• Overlap Testing

34. Collision Response(1)
• Contact Point
– EE (Edge-Edge)
– FV (Face-Vertex)
– GJK
• Normal
• Penetration

35. Collision Response(1)
• Contact Point
– EE (Edge-Edge)
– FV (Face-Vertex)
– GJK
• Normal
• Pentration

36. Collision Response(2)
• Colliding
– Bouncing
• Resting
– Rolling
– Sliding

37. Collision Response(2)
• Colliding
– Bouncing
• Resting
– Rolling
– Sliding

38. Constraint
• Joint
– Pin Joints
– Hinge
• Angular Constraints
• Distance Constraints, ...

39. PhysX-Joint
• spherical joint
• revolute joint
• prismatic joint
• cylindrical joint
• fixed joint
• distance joint
• point in plane joint / point on line joint
• pulley joint
• d6

40. PhysX-Joint
• spherical joint
• revolute joint
• prismatic joint
• cylindrical joint
• fixed joint
• distance joint
• point in plane joint / point on line joint
• pulley joint
• d6

41. PhysX-Joint
• spherical joint
• revolute joint
• prismatic joint
• cylindrical joint
• fixed joint
• distance joint
• point in plane joint / point on line joint
• pulley joint
• d6

42. PhysX-Example Review
• 예제 : SampleBoxes
• InitNx
– Initialize PhysicsScene => gPhysicsSDK
– CreateScene => gScene
– Create Ground => gScene->createActor
• RenderCallback
– Simulate
– GetResult/Render All actors => actor->getGlobalPos
– FetchSimulation => flushScream, fetchResult
• CreateCube
– shapes.pushBack
– gScene->createActor

43. More
• Breaking
• Force Field
• Character Controller
• Raycast/SweepTest
• Multithreading Model

44. Reference
• http://www.essentialmath.com
• 게임물리바이블,David H Everly, 사이텍미디어